Usage

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Arguments

Y

vector of responses.

Xend

matrix of the endogenous variables, i.e. covariates that
are correlated with the regression's error term.

Xex

matrix of the exogenous variables, i.e. covariates that are
uncorrelated with the regression's error term. Default =
NULL, i.e. no exogenous variables are present in the model.

Zinst

matrix of instruments, variables correlated with the
endogenous covariates, but uncorrelated with the error term. The
number of instrumental variables needs to be larger than or equal to
the number of endogenous covariates.

dummies

matrix of exogenous dummy covariates, i.e.,
where each D_i are 0–1 vectors.

method

the method to be used. The "S-est" method
(default) is based on the S-estimator of multivariate location and
covariance, and "classical" method is based on the sample
mean and covariance and the resulting estimator is equivalent to the
two-stage least squares estimator (2SLS). See Details
section.

Details

For method "S-est", RIV is constructed using the
robust multivariate location and scatter S-estimator based on
the Tukey's biweight function (see CovSest).

If RIV is computed using the S-estimator, its variance-covariance
matrix is estimated based on the empirical influence function. See
references for more details.

For method "classical", the estimator is the classical
instrumental variables estimator based on the sample mean and sample
variance-covariance matrix (also known as the two-stage least squares estimator, 2SLS).

If the model contains dummy variables (i.e., dummies != NULL),
RIV is computed using an iterative algorithm called "L_1-RIV".
Briefly, L_1-RIV estimates the coefficients of the dummies using
an L_1-estimator and the coefficients of the continuous
covariates using the original RIV. See Cohen Freue et al. for more
details.

Value

A list with components:

Summary.Table

Matrix of information available about the
estimator. It contains regression coefficients, and, for
method = "S-est" and "classical" only, columns
for the standard error, t-statistic, and p-value.

VC

MD

Squared Mahalanobis distances of each observation to the
multivariate location S-estimator with respect to the scatter
S-estimator (only computed if method = "S-est").

MSE

vector of three components, computed only if method
= "S-est" or "classical":

sigma.hat1: the mean square error estimation;

sigma.hat2: the mean square error estimation taking into
account the weights associated to each observation (only
computed if method = "S-est" and coefficents of
endogenous variables are exactly identified, i.e., the number of
instruments is equal to the number of endogenous variables);